Three-dimensional chess is a good example of a chess variant. Three-dimensional variants have existed since the late 19th century. One of the oldest versions still regularly played is Raumschach, invented in 1907 by Ferdinand Maack and played on a 5x5x5 board.
However, the most familiar variant to the general public in the early 21st century is the Star Trek game which can be seen on a lot of Star Trek movies and TV series, starting from the original one throughout the rest of the series. The same or different variant of 3-D chess is also seen in Ginga Eiyu densetsu, a Japanese sci-fi novel.
The original Standard Rules of this game were developed by Andrew Bartmess in 1976, while the chessboard set was made popular by inclusion in the Starfleet Technical Manual by Franz Joseph Schnaubelt. Schnaubelt did not design the original chessboard.
There also is a GNU FDL manual written in Italian by Marco Bresciani, which presents the complete standard set of rules with instructions on how to build a chessboard and many other things. This manual is available through the Star Trek Italian Club (see link at end), for members only.
There is a lot of software for playing three-dimensional chess, although no software completely uses Andrew Bartmess's Standard Rules.